Browsing by Subject "Nusselt number"

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    High-rayleigh-number thermal convection of compressed gases in inclined rectangular enclosures of varied aspect ratios
    (2019-08) Madanan, Umesh
    In the present study, heat transfer measurements and flow visualization are carried out for high-Rayleigh-number thermal convection in horizontal and tilted rectangular enclosures. The heat transfer measurements are performed for a wide range of Rayleigh numbers (1.85×10^6 ≤ Ra ≤ 1.04×10^11) using enclosures of different aspect ratios (AR = 1, 3, 6, and 10) and angles of inclination (ϕ = 0°, 30°, 60°, 90°, 120°, and 150°). Here, high Rayleigh numbers are achieved using compressed nitrogen and argon. Another set of experiments is conducted using sidewalls made of three materials having different thermal conductivities (Styrofoam, Plexiglas, and high-density polyethylene) to assess the effect of sidewall conductance heat loss on the horizontal enclosure free convection. Additionally, a z-type shadowgraph visualization is employed at angles of inclination between 0° and 90° to characterize the buoyant flow and validate the observed heat transfer trends. Firstly, the effect of sidewall conductance heat loss on Nusselt number is examined by performing nearly identical sets of experiments using horizontal cubical enclosures with sidewalls made of three different materials. The results from these experiments reveal a higher difference (∆Nu) between the sidewall-uncorrected Nusselt number (Nu_net) and the sidewall-corrected Nusselt number (Nu_c) than that obtained when using a traditional empty-cell gradient assumption. Thus, a semi-analytical model is proposed to estimate the sidewall-corrected Nusselt number, given the corresponding uncorrected values, which is found to predict this experimentally observed difference in Nusselt numbers to within 11% (when Wn ≥ O(1)). Another empirical model is also proposed to estimate the sidewall-corrected Nusselt numbers for smaller wall numbers (or, Wn → 0) and the predicted ∆Nu values for this case are found to be within 1.5% of the corresponding experimental data. Additionally, the Nusselt numbers for an ideal zero-thermal-conductivity sidewalls case are also estimated by extrapolating the corresponding Nu_net values obtained from the experiments. Further experiments in the present study are conducted after taking into consideration this effect of the sidewall conductance heat loss and using a sidewall material of low wall number (Styrofoam). Another set of experiments is carried out to determine the correlating equations for Nusselt number, computed from steady-state electrical power input and temperature measurements, in terms of the studied variables for the horizontal and tilted enclosures. For the horizontal enclosure problem, this correlation is found to closely follow the classical 1/3^rd scaling relation between Nusselt number and Rayleigh number. For the tilted enclosure problem, a set of single-parameter (Nu = f(Ra)) and two-parameter (Nu = f(Ra,AR)) correlating equations are proposed to estimate the average Nusselt number at any of the investigated angles of inclination. The proposed correlations are found to predict the experimental values with reasonable accuracy. The effect of aspect ratio on Nusselt number is assessed by performing experiments with varied aspect ratios at a fixed Rayleigh number. For inclined enclosures, at any angle of inclination and a given Rayleigh number, Nusselt number is observed to follow a decreasing trend with an increase in the aspect ratio. Moreover, this decreasing trend is observed to gradually amplify as the angle of inclination is increased, with a negligible effect at an angle of inclination of 0° (or, for the horizontal enclosure problem) and a prominent effect at an angle of inclination of 90° (or, for the vertical enclosure problem). The effect of angle of inclination on Nusselt number is also examined by performing experiments with varied aspect ratios and Rayleigh numbers. Nusselt number is found to decrease with an increase in the angle of inclination and this decreasing trend remains qualitatively the same for all the studied aspect ratios and Rayleigh numbers. There is a substantial drop observed in the Nu values between the angles of inclination 0° and 90°, whereas, in general, this drop is found to be minimal between the angles of inclination 90° and 150°. For any given aspect ratio, this variation in the Nu values is observed to become more prominent as the Rayleigh number increases. The flow visualization studies for the horizontal enclosure problem indicate the presence of thermal plumes together with a large scale flow. These thermal plume eruptions are found to move across the central region (or, core) of the enclosure toward the opposing active wall. The frequency of the thermal plume eruptions and the velocity of the large scale flow are observed to increase with an increase in the Rayleigh number. For tilted enclosures, mixing within the core region is found to decrease as the angle of inclination is increased. Thus, for the vertical enclosure problem, the most prominent feature is an unperturbed core, with traveling wave-like structures over the boundary layers on the hot and cold vertical walls. In addition, the buoyant flow velocity is observed to decrease with an increase in the angle of inclination.